A GaAs single crystal is widely used as a substrate of an element to be used, for example, in optical communication and microwave communication. Further, since it has high electron mobility, a GaAs integrated circuit is intensively being developed.
The GaAs single crystal is practically grown by a boat method or by a liquid encapsulated Czochralski method (hereinafter referred to as "LEC method"). Although there are some other methods for growing the GaAs single crystal, they are laboratory methods and not commercially employed.
(a) LEC Method
By this method, a GaAs single crystal ingot having a circular cross section is prepared and thus material loss is little. In addition, the ingot having a large diameter is easily prepared. Therefore, this method is commercially attractive.
Since the single crystal is grown at a temperature higher than 1,200.degree. C. under a pressure of 2 to 100 atm. by the LEC method, vigorous convection of environmental gas (eg. nitrogen or argon) is generated. B.sub.2 O.sub.3 encapsulation which prevents dissipation of As has a heat insulating effect. Thus, temperature gradient near an solid-liquid interface reaches an order of 50.degree. to 200.degree. C./cm, and large thermal strain is generated in the grown single crystal, which results in dislocation in the crystal.
Degree of lattice defect in the single crystal is evaluated by etch pit density (hereinafter referred to as "EPD"). The etch pit is a pit which appears when the surface of the single crystal is polished and etched with an appropriate etchant (eg. molten KOH) and corresponds to the lattice defect. EPD is defined as number of the pits per unit area, which is counted by means of a microscope. EPD is sometimes referred to as "dislocation density".
The dislocation density of the GaAs single crystal of 2 to 3 inches in diameter prepared by the LEC method is very high and, for example, from 10,000 to 100,000, which is 10 to 100 times that of a GaAs single crystal prepared by the boat method.
The GaAs single crystal is promising particularly as a substrate of a field-effect transistor (hereinafter referred to as "FET"). This is because a high speed device can be produced with the GaAs single crystal, since it has higher electron mobility than silicon. Many FETs are formed on a wafer by a wafer process to produce an integrated circuit. In such case, all the FETs should have substantially the same pinch-off voltage, which is input voltage when output voltage of FET changes between 0 and 1. If each FET has different pinch-off voltage, it is not suitable for the production of the integrated circuit. The FETs formed on the conventional GaAs substrate has diversely varying pinch-off voltage. This is due to nonuniformly distributed dislocations present in the single crystal.
For the production of the GaAs integrated circuit, it is essential to use a semi-insulating GaAs single crystal which has a very little dislocation density and in which the dislocation is homogeneously distributed.
The generation of dislocation is due to large temperature gradient near the solid-liquid interface. Since a solidified fraction is rapidly cooled by radiation and convection, it shrinks and generates thermal strain in it, which, in turn, generates and propagates the dislocation. Not only the unstability of the solidified fraction but also unstability of the raw material melt causes trouble. The GaAs raw material melt is contained in a crucible which is heated by a carbon heater provided with around it. The carbon heater generates heat by means of a resistor. Since the crucible is heated by the thus generated heat, the temperature of the crucible is higher than that of the raw material melt. Then, the temperature of the upper portion of the raw material melt is not necessarily the same as that of the lower portion. Usually, the temperature of the lower portion which contacts with the crucible is higher than that of the upper portion. A large amount of heat is transferred from the lower portion to the upper portion by heat conduction, thereby the temperature difference is decreased to restore the thermal stability in the melt.
However, when the temperature of the lower portion is too high, that is, the temperature difference is too large, the density of the melt in the lower portion becomes small and the melt tends to rise by convection. Namely, the thermal conduction and convection transfer excessive heat in the lower portion to the upper portion. So long as the thermal conduction predominates, the heat transfer is stationary. However, if the convection predominates it is not stationary.
The ratio of the thermal conduction to the convection is evaluated by Rayleigh number R of the formula: EQU R=g.alpha..beta.h.sup.4 /.nu.k (1)
wherein g is gravitational acceleration, .alpha. is a coefficient of cubic expansion of a liquid, .beta. is temperature gradient in the vertical direction (the temperature of the lower portion being higher), .nu. is a coefficient of kinetic viscosity, k is a diffusion coefficient and h is a height of the melt. The diffusion coefficient k is a value obtained by dividing thermal conductivity by the product of density and specific heat.
When the Rayleigh number exceeds a certain critical value, the state of the liquid changes from a stationary condition to a random one. The critical value depends on a shape of a container. It is to be noted that the Rayleigh number is inversely proportional to the coefficient of kinetic viscosity. In a narrow space like the crucible, as its bottom is heated, the temperature gradient increases and the Rayleigh number reaches the critical value. Then, the content becomes the random condition so that the convection predominates the thermal conduction. By the convection, heat is transferred to the upper portion, thereby the temperature gradient decreases. Therefore, the Rayleigh number diminishes and the melt tends to restore the original stationary condition.
As discussed in the above, the energy of the convection is not always constant but rather varies. Although the temperature distribution in the crucible vigorously changes due to the convection, the temperature of the upper portion of the melt periodically changes due to variation of the energy of convection. The temperature at the solid-liquid interface is equal to the melting point of GaAs, i.e. 1,238.degree. C. However, the level of the interface changes up and down due to the variation of the convection.
(b) High Magnetic Field LEC Method
Due to change of the level of the solid-liquid interface, the growth rate of the single crystal being pulled up varies.
To prevent the variation of the growth rate in the LEC method, it is proposed to suppress the convection in the raw material melt by applying a high magnetic field to the raw material melt (cf. Japanese Patent Kokai Publication (unexamined) No. 120592/1983).
It is presumed that As and Ga atoms moves as charged particles in the melt. The motion of the charged particle is disturbed by the applied magnetic field and the particles cannot go straight on due to Lorentz force to be applied to them, which means practical increase of viscosity. Then, the Rayleigh number decreases and the strength of the convection weaken, so that the thermal conduction predominantly contributes to the thermal equilibrium.
The above method may be called a "high magnetic field LEC method".
When the single crystal pulled up by this method is sliced along a plane including the growth axis and AB (Abrahams Buiocchi) etched with a mixture of AgNO.sub.3, CrO.sub.3, HF and water to view growth striations, curved stripes almost disappear which are observed in a single crystal pulled up by the conventional method.
The curved stripes are parallel stripes with distance of several microns to several hundred microns and appear in the vertical cross section. They are also called as "growth striations".
Since the growth striations appear also in a non-doped GaAs single crystal, they may be due to the periodical temperature fluctuation at the solid-liquid interface.
Although it is reported that the growth striations disappear in the GaAs single crystal pulled up by the strong magnetic field LEC method, EPD is not improved by this method. According to the hitherto reported data, it cannot be concluded that EPD is decreased by this method.
This may be because that completeness of the experimental facility and technique were insufficient and thus EPD might not be improved. In addition, the applied magnetic field might be too weak.
The present inventors, however, think that the strong magnetic field LEC method cannot effectively improve EPD of the GaAs single crystal. Our ground is as follows:
The strong magnetic field method can reduce the the temperature fluctuation at the solid-liquid interface. However, the dislocation is not immediately generated at the interface but is generated in the solidified fraction pulled up from the interface. Thus, the suppression of the convection in the liquid phase does not lead to the decrease of the dislocation.
In the solidified fraction, the single crystal shrinks. However, the shrinkage is not uniform since the temperature does not uniformly lower in the radial direction. Due to this ununiform shrinkage, the dislocation is generated.
(c) LEC Method with Impurity Doping
It is known that the quality of the GaAs single crystal is improved by doping an impurity. However, the reason why the impurity improves the quality of the single crystal is not theoretically explained. There are many proposals and theories.
There is no definite opinion on which impurity is the best. In addition, the reported data are hardly reproducible and the experiments cannot be traced by others.
(d) Willardson's Theory
Willardson et al proposed to dope the III-V compounds with an impurity so as to increase the electron mobility (cf. U.S. Patent No. 3,496,118 to Willardson et al.). They concluded that the appropriate impurities are Te, Sb, Bi and Pd.
Willardson's theory may be called a "freezing point lowering theory".
When a solute is dissolved in a solvent, a freezing point of the solvent is lowered. Accordingly, the melting point, i.e. freezing point of GaAs is lowered by the doping of the impurity. With the lower melting point, the thermal strain decreases and the single crystal having less defects is prepared. Thus, the more greatly the melting point lowered, the better. Since it is not desirable for the single crystal to contain the impurity, they concluded that the impurity should have the distribution coefficient k much less than 1 (one).
According to Willardson et al, in case of GaAs melt, the distribution coefficients of Sd, Pb, Te and Bi are 0.016, 0.0002, 0.059 and 0.0005, respectively. Therefore, they select the impurity having the distribution coefficient k less than 0.02.
Willardson et al say that the melting point of the GaAs melt can be lowered by 100.degree. C. or more by doping the impurity.
The present inventors think the freezing point lowering theory may be wrong since the melting point of the raw material cannot be lowered by 100.degree. C. or more by the the addition of the impurity.
(e) Mil'vidsky's Theory
Mil'vidsky et al proposed to dope a semi-conductive single crystal with an impurity to decrease defects of the single crystal (cf. Journal of Crystal Growth, 52, 396-403 (1981)).
They think that the dislocation in the single crystal is generated by shear stress due to the thermal strain generated during the cooling step, and that the impurity increases the critical shear stress so that the single crystal becomes harder.
According to Mil'vidsky et al, the shear stress increases in proportional to a value obtained by dividing square of the difference between the volume of the matrix element and that of the impurity element by the diffusion coefficient k.
Mil'vidsky et al describe EPD of the GaAs single crystal of 20 to 25 mm in diameter pulled up by the LEC method. When Te is doped in an amount of 10.sup.19 /cm.sup.3, EPD decreases to 10/cm.sup.2. According to them, next to Te, In and Sn are preferred.
Mil'vidsky et al think that the dislocation linearly propagates but is blocked by the impurity which is present on the propagation line.
The present inventors cannot agree with Mil'vidsky et al.
In a wafer sliced from the single crystal, EPD is large at its periphery and center.
The shape of the single crystal prepared by the LEC method is cylindrical and thus the shear stress at the center should be zero. If the shear stress has great influence on the dislocation, the reason why EPD is large at the center is not explained by the Mil'vidsky theory.
The projection of the stress in the (111) plane on the (110) direction has W figure distribution and thus is not zero at the center. This is the projection of the whole stress. However, the stress at the center is compressive stress.
The propagation of the dislocation line could be blocked by the impurity in the amount of several percents to several tenths percent, but it is unbelievable that EPD of 100,000/cm.sup.2 is decreased to 100 to 1,000/cm.sup.2.
In addition, the single crystal pulled up by Mil'vidsky et al has a diameter of 20 to 25 mm, which is not suitable for commercial production. If a single crystal having a diameter of 2 to 3 inches is pulled up under the same conditions as such small one is pulled up, the produced single crystal should have large EPD.
(f) Jacob's Experiments
G. Jacob et al disclosed isoelectronic doping of GaAs and InP (cf. Journal of Crystal Growth, 61, 417-424 (1983)).
They pulled up GaAs doped with P, B, In or Sb by the LEC method to obtain 70 to 100 g of a single crystal having a diameter of 15 to 25 mm.
According to their experiments, the single crystal doped with P or B has EPD of 10,000 to 100,000/cm.sup.2, which is substantially the same as that of the non-doped one.
When In is doped in GaAs in the form of InAs by 10% by weight, the upper two thirds form a single crystal in which substantially no dislocation is present except a few dislocations in the (100) direction.
Sb is doped as a simple substance or in the form of GaSb. When it is doped in an amount of 5% by weight, the upper one third forms a single crystal in which substantially no dislocation is present except a few dislocations in the (100) direction.
Jacob et al conclude that the distribution coefficient is preferably larger than 1 (one), which is contrary to the conclusion of Willardson et al. When the distribution coefficient k is larger than 1, the whole crystal forms a single crystal. However, when the distribution coefficient k is smaller than 1, only one half or third of the crystal forms a single crystal. This is because the GaAs melt is supercooled and the bottom portion does not form single crystal if the distribution coefficient is smaller than 1.
In any event, the single crystal pulled up by Jacob et al using the LEC method has a small diameter and light weight and thus is not commercially interesting. They say that the single crystal has substantially no dislocation, but it is true for the upper portion of the produced single crystal, since only that portion forms the single crystal.
(g) Jacob's Theory
Jacob proposed some methods for decreasing the lattice defects in GaAs (cf. G. Jacob, "How to Decrease Defect Densities in LEC SI GaAs and InP Crystal", Proceeding 2nd International Conference on Semi-Insulating III-V Compounds, Evian. 1982). In this literature, Jacob proposed following three methods:
(i) Liquid Encapsulated Kyropoulos (LEK) method
(ii) Necking
(iii) Impurity doping.
The LEK method is firstly proposed by Jacob. Since, in the LEC method, the crystal is pulled up out of the liquid encapsulation of B.sub.2 O.sub.3, it is suddenly cooled. On the contrary, in the LEK method, the crystal is cooled to solidify in the liquid encapsulation.
Since the B.sub.2 O.sub.3 melt has small temperature gradient and a heat insulation effect, the temperature distribution in the crystal is rather homogeneous. Therefore, the thermal strain is small so that the single crystal having less EPD is pulled up.
Since the single crystal is solidified in the liquid encapsulation by the LEK method, it is shorter than the depth of the encapsulation. Therefore, the pulled up single crystal ingot is a flat one having a larger diameter but short length. The ingot actually pulled up by Jacob had a diameter of 10 cm and a length of 3 cm.
Jacob says that EPD in the single crystal prepared by the LEK method is about one tenth of that prepared by the LEC method. However, only a small number of wafers are sliced from the ingot prepared by LEK method since the prepared ingot has a short length.
If the depth of the B.sub.2 O.sub.3 melt is deepen and the diameter of the crucible is made large, it is possible to prepare a long ingot. However, the single crystal of larger diameter encounters quite large viscous resistance, since the B.sub.2 O.sub.3 melt has large viscosity. Generally, the single crystal is pulled up with rotation to make the outer diameter uniform. But, since the large viscous resistance makes it difficult to rotate the single crystal, it is difficult to prepare a long crystal. Therefore, the LEK method is not commercially advantageous.
Necking is one of the well known methods, in which the diameter of the single crystal adjacent to a seed crystal is made small and then gradually thicken to form a shoulder. The necking can exclude outward the dislocation propagated from dislocation source included in the seed crystal.
As examples of the impurity doping method, Jacob pulled up GaAs doped with P, In, Sb or B by the LEC method. Among them, one doped with P or B forms a single crystal. However, it has EPD of 10,000 to 100,000/cm.sup.2, which is as large as the conventional one.
When In or Sb is doped, the upper two thirds or one half forms single crystal and a part of it contains no dislocation. However, the single crystal has a diameter of 20 mm and a length of 50 to 60 mm.
Jacob says that the critical shear stress defined by Mil'vidsky et al has two meanings, one of which is shear stress for firstly generating the dislocation and another of which is shear stress for propagating the once generated dislocation. These two kinds of shear stress should be distinguished. According to Jacob, the former may be ten times or more larger than the latter.
Jacob explains the reason for hardening of the single crystal by impurity doping of, for example, Si as follows:
In some portions, Ga site is vacant, which is referred to as "Ga vacancy", and in some other portions, the Ga site is replaced by Si, which is referred to as "replaced Si".
When GaAs is aged at a temperature of 400.degree. to 800.degree. C., the hardness of the single crystal increase as time passes. The reason for this is that the replaced Si moves around and interacts with the Ga vacancy to form a replace Si-Ga vacancy pair. By this interaction, the lattice is reinforced.
Similarly, when GaAs is doped with the impurity such as S, Te, Ge, Sn, etc., the impurity replacing the Ga site and the Ga vacancy interact to reinforce the lattice bonding.
The present inventors are against Jacob.
The Ga vacancy should have minus charge since it is formed by removal of Ga from the site at which trivalent Ga should be present. On the other hand, since Si, S, Te, Ge or Sn replacing the Ga site liberates an electron as a free electron, it should have plus charge. Thus, the Coulomb force between the plus and minus charges reinforces the lattice bonding.
However, the reason why the Ga site is replaced with S and Te but the As site is not is uncertain. In addition, such phenomenon occurs only when As is present in excess and Ga is insufficiently present.
Such Coulomb force is not generated by In and Al which is isoelectronic with Ga. Therefore, the Jacob's theory is totally invalid for In and Al. However, the experimental data for In and Al strangely support the theory.
In addition, it is questionable whether the reinforcement of the lattice bonding has any influence on the decrease of dislocation.
Mil'vidsky et al explain that the impurity doping increases the critical shear stress so that the dislocation is suppressed. However, the reinforcement of the lattice bonding does not necessarily lead to the suppression of dislocation. Since the lattice structure is present in the dislocation domain, the reinforcement by Coulomb force also augments the force which generates the dislocation.